Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability

Mathew A. Johnson (1) , Pascal Noble (2) , Luis Miguel Miguel Rodrigues (2) , Kevin Zumbrun (3)

1 Department of Mathematics [Lawrence, Kansas]
2 ICJ - Institut Camille Jordan
3 Department of Mathematics IU

Extending results of Johnson and Zumbrun showing stability under localized (L1 ) perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. The main new ingredient is a detailed analysis of linear behavior under modulational data u_x(x)h0 (x), where u is the background profile and h0 is the initial modulation.

Domaines: Equations aux dérivées partielles [math.AP]

Mathew A. Johnson, Pascal Noble, Luis Miguel Miguel Rodrigues, Kevin Zumbrun. Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability. Archive for Rational Mechanics and Analysis, 2013, 2, pp.693-715. ⟨hal-00943577⟩